1.

Which one of the following statements is not a tautology?1. (p ∨ q) → (p ∨ (~q))2. (p ∧ q) → (~p) ∨ q3. p → (p ∨ q)4. (p ∧ q) → p

Answer» Correct Answer - Option 2 : (p ∧ q) → (~p) ∨ q

p

q

~q

p ∨ ~q

~p

p ∧ ~q

T

T

F

T

F

F

T

F

T

T

F

T

F

T

F

F

T

F

F

F

T

T

T

F

p

q

p ∨ q

p → p ∨ q

p ∧ q

p ∧ q → p

T

T

T

T

T

T

T

F

T

T

F

T

F

T

T

T

F

T

F

F

F

T

F

T

p

q

~p ∨ q

(p ∧ q) → (~p) ∨ q

(p ∨ q) → (p ∨ (~q))

T

T

T

T

T

T

F

F

T

T

F

T

T

T

F

F

F

T

T

T

A tautology is a formula or assertion that is true in every possible interpretation. So, by the truth table (p ∨ q) → (p ∨ (~q)) statement is not a tautology.

Atautologyis a statement that is alwaystrue, no matter what. If you construct atruth tablefor a statement and all of the column values for the statement aretrue(T), then the statement is a tautologybecause it's alwaystrue!


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